Pseudo-Bautin Bifurcation in 3D Filippov Systems

Abstract

Consider a piecewise linear dynamical system in [Formula: see text], divided by a switching plane, with the Teixeira Singularity (TS). Under the antiparallelism hypothesis, it is known that the system undergoes the so-called pseudo-Hopf bifurcation (pH). In this paper, we consider a particular position of the antiparallel vectors to yield a two-parametric unfolding of the TS. The bifurcation analysis gives us, besides the curve of pH bifurcation points, a curve of saddle-node bifurcation points for crossing limit cycles. We call this phenomenon the pseudo-Bautin bifurcation, since it exhibits the exact same behavior as the Bautin bifurcation for smooth dynamical systems.